Question: Simplify; express your answer in exponential form. Assume $t\neq 0, k\neq 0$. $\dfrac{{(t^{-3})^{-3}}}{{(t^{4}k^{-2})^{-1}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{-3}}$ to the exponent ${-3}$ . Now ${-3 \times -3 = 9}$ , so ${(t^{-3})^{-3} = t^{9}}$ In the denominator, we can use the distributive property of exponents. ${(t^{4}k^{-2})^{-1} = (t^{4})^{-1}(k^{-2})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(t^{-3})^{-3}}}{{(t^{4}k^{-2})^{-1}}} = \dfrac{{t^{9}}}{{t^{-4}k^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{9}}}{{t^{-4}k^{2}}} = \dfrac{{t^{9}}}{{t^{-4}}} \cdot \dfrac{{1}}{{k^{2}}} = t^{{9} - {(-4)}} \cdot k^{- {2}} = t^{13}k^{-2}$.